FM for Actuaries

132 CHAPTER 4
Thus, the smaller the DPP, the earlier the project recovers its investment. Hence,
a capital budgeting criterion is to choose the project with the lowest DPP. The
example below illustrates this criterion.
Example 4.18: Consider the two projects in Example 4.16. Discuss the choice
of the two projects based on the DPP criterion.
Solution: For Project B, as the most substantial cash flow generated is at the end
of the project duration, the DPP of the project is 15 years. For Project A, Table 4.3
summarizes the results for several required rates of interest R R .
Table 4.3:
NPV of Project A
R R t NPV(t) DPP
0.03 12 –4.5996 13
13 63.4955
0.04 13 –1.4352 14
14 56.3123
0.05 14 –10.1359 15
15 37.9658
0.06 15 –28.7751 16
16 10.5895
For required rates of interest of 3%, 4%, 5% and 6%, the DPP of Project A are,
respectively, 13, 14, 15 and 16 years. When the required rate of interest is 6%,
Project B has a negative NPV and the DPP is not defined. When the required
interest rate is 5%, Project B has the same DPP as Project A, namely, 15 years. For
other required rates of interest considered, the DPP of Project A is shorter.
If R R in (4.21) is set equal to zero, the resulting value of t at which NPV(t)
first becomes positive is called the payback period. Although a project appraisal
method may be based on the minimum payback period, this method lacks theoretical
rigor as the time value of money is not taken into account.
4.8 Summary
1. The internal rate of return is the discount rate that equates the present value
of cash outflows to the present value of cash inflows for a project. It is a